Cruciform Specimens Research Articles

Experimental and numerical investigation of differential hardening of cold rolled steel sheet under non-proportional loading using biaxial tensile test

Strain path change is common phenomenon during industrial sheet metal forming processes. These strain paths can be proportional and non-proportional in nature. To enable strain path change in a single experiment is key challenge faced by many researchers. To predict deformation behavior accurately during such strain paths, it is required to represent initial yielding, the evolution of subsequent yield surface and hardening behavior precisely. This work deals with the mechanical characterization of Interstitial Free High Strength Steel (IFHS) during multi-axial proportional and non-proportional loading for the determination of yield surface evolution and strain hardening behavior. A set of tensile tests at various orientations with respect to the rolling direction and in-plane biaxial tests using cruciform specimens for various linear and bi-linear stress ratios were performed on as-received materials. It was found that at the onset of stress path change, the stress strain curve shows a change in the hardening rate for rolling and transverse directions of the biaxial specimen due to the change in active slip systems. To predict this behaviour various yield criterion like von Mises, Hill's 48 and Yld2000-2d were used. The experimental results show that the mechanical behavior of the subjected specimen deviates from isotropic behavior predicted by the von Mises and anisotropic behavior predicted by the Hill's 48 yield criterion. The initial yield loci measured by biaxial testing machine is in good agreement with what is predicted by Yld2000-2d yield criterion. However, it was observed that such phenomenological models were unable to capture the observed deformation behaviour. It is also shown that classical Crystal Plasticity Finite Element Method (CPFEM) can capture change in strain hardening rate during non-proportional deformation for few cases reasonably well while in few cases it could not predict.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

Concentric and eccentric compression performance of multiple-cell cruciform CFSTs

Multiple-cell cruciform concrete-filled steel tube is a novel and efficient category of conventional cruciform concrete-filled steel tubes, mainly suitable for structures requiring high resistance and excellent seismic performance. This paper presents a test study of ten multiple-cell cruciform concrete-filled steel tube specimens, including six stub specimens and four slender specimens under compression. The experiment comprises the following key parameters: tube width-to-thickness ratio, length-to-breadth ratio, and eccentricity ratio. The influence of these factors on peak resistance, failure pattern and ductility were investigated by discussing and analyzing the failure procedure, load-displacement relationships, load-lateral deflection graphs and load-strain relationships. The test results demonstrated that: (1) local buckling was deferred, and the peak resistance was improved for specimens with smaller width-to-thickness ratio; (2) specimens with increment in length-to-breadth ratio or eccentricities had lower compression capacities; (3) the configuration of multiple-cell steel tubes improved the constraint effect significantly. Further, the finite element simulation was performed to determine the behaviors of the specimens and was validated with test results. Based on the parametric analysis, the N–M relationships were obtained considering parameters as the width-to-thickness ratio, slenderness ratio, eccentricity, steel grade and concrete strength. The concentric and eccentric compression capacity of multiple-cell cruciform concrete-filled steel tubes was predicted by current design codes. At last, the equations to calculate the compression capacity under concentric or eccentric loads were suggested, which were verified by the experimental and simulation results.

Planar‐biaxial low‐cycle fatigue behavior of the nickel‐base alloy Inconel 718 at elevated temperatures under selected loading conditions

AbstractThe isothermal planar‐biaxial fatigue behavior was studied for two different disk batches of nickel‐base superalloy Inconel 718 using cruciform specimens at 400°C and 630°C under equi‐biaxial and shear loading. Additionally, non‐proportional tests were performed. The planar‐biaxial test results were compared with uniaxial reference tests using the von Mises equivalent strain hypothesis, a shear strain parameter of the critical plane, and a modified crack‐opening‐displacement strain range approach. Additionally, the crack initiation mechanism was analyzed. Using a modified crack‐opening‐displacement strain range approach, the low‐cycle fatigue lifetimes of the proportional planar‐biaxial tests (i.e., lifetimes up to 40,000 cycles) were described within a scatter band of two. Thus, it was better than using the equivalent strain of von Mises or a shear strain parameter. The fatigue crack initiation took place at oxidized primary carbides at the surface. The crack paths were presented.

Advances in Cruciform Biaxial Testing of Fibre-Reinforced Polymers.

The heterogeneity and anisotropy of fibre-reinforced polymer matrix composites results in a highly complex mechanical response and failure under multiaxial loading states. Among the different biaxial testing techniques, tests with cruciform specimens have been a preferred option, although nowadays, they continue to raise a lack of consensus. It is therefore necessary to review the state of the art of this testing methodology applied to fibre-reinforced polymers. In this context, aspects such as the specific constituents, the geometric design of the specimen or the application of different tensile/compressive load ratios must be analysed in detail before being able to establish a suitable testing procedure. In addition, the most significant results obtained in terms of the analytical, numerical and experimental analyses of the biaxial tests with cruciform specimens are collected. Finally, significant modifications proposed in literature are detailed, which can lead to variants or adaptations of the tests with cruciform specimens, increasing their scope.

Optimization of a cruciform specimen for fatigue crack growth under in and out-of-phase in-plane biaxial loading conditions

Mixed-mode loading conditions are present in different mechanical components. Understanding the influence of in-plane biaxial loading paths parameters allows for fatigue crack growth (FCG) prediction and component fatigue life assessment. Cruciform specimens are used to simulate these conditions, but large specimen dimensions are required in order to keep crack propagation unaffected by specimen geometry. This article describes the procedure used to optimize a new cruciform specimen geometry, with small dimensions. Having identified the specimen arms fillet as a major source of crack growth interference, this effect was kept to a minimum, while using arm slots with different widths and lengths. Individual slot dimensions were optimized using a Direct MultiSearch (DMS) algorithm, minimizing the stress intensity factor (SIF) difference between the optimal specimen and an infinite plate. FCG on the optimized specimen was simulated under in and out-of-phase loading conditions. Due to crack closure effects, fatigue propagation under fully out-of-phase loading is less sensitive to specimen geometry. Therefore, the final geometry was chosen considering the required biaxial loading ratio under in-phase loading.

Stability of cruciform specimens for fracture tests under compression

Cruciform specimens have been developed in the last decades in order to evaluate the fatigue and fracture material behaviour under biaxial stress fields. These evaluations have been generally conducted under positive load ratios, so as to prevent the potential buckling of these generally thin specimens.This paper reports a numerical investigation on the stability of two cruciform specimens in order to provide useful information for the design of biaxial fracture tests under both tension and compression. Two cruciform geometries were selected among those widely accepted in literature and slightly modified so as to apply equal boundary conditions. FEM simulations were performed under tensile and compressive loading conditions by considering geometric imperfections based on the superposition of the buckling modes. Results were cross-compared in terms of stress fields, load–displacement curves, stress intensity factors and critical loads along crack propagation. Guidelines of general validity were derived.

An Equal-Biaxial Test Device for Large Deformation in Cruciform Specimens

An Equal-Biaxial Test Device for Large Deformation in Cruciform Specimens

Experimental and Numerical Investigation of High-Temperature Multi-Axial Fatigue

Abstract Gas turbines and aircraft engines are dominated by cyclic operating modes with fatigue-related loads. This may result in the acceleration of damage development on the components. Critical components of turbine blades and disks are exposed to cyclic thermal and mechanical multi-axial fatigue. In this work, planar-biaxial low-cycle-fatigue (LCF) tests are conducted using cruciform specimens at different test temperatures. The influence on the deformation and lifetime behavior of the nickel-base disk alloy Inconel 718 is investigated at selected cyclic proportional loading cases, namely, shear and equi-biaxial. The calculation of the stress and strain distribution of the cruciform specimens from the experimental data is difficult to obtain due to complex geometry and temperature gradients. Therefore, there is a need for finite element (FE) Simulations. A viscoplastic material model is considered to simulate the material behavior subjected to uniaxial and the selected planar-biaxial loading conditions. At first, uniaxial simulation results are compared with the uniaxial experiment results for both batches of IN718. Then, the same material parameters are used for simulating the biaxial loading cases. The prediction of FE simulation results is in good agreement with the experimental LCF test for both shear and equi-biaxial loadings. The equivalent stress amplitude results of the biaxial simulation are compared with the uniaxial results. Furthermore, the lifetime is calculated based on the stabilized cycle from the simulation and by using Crossland and Sines multi-axial stress-based approaches. The Crossland model predicts fatigue life significantly better than the Sines model. Finally, the simulated lifetime results are compared with the experimental lifetime.

On the influence of different in-plane biaxial loading conditions over FCG lives

In-plane biaxial loading conditions have a strong influence over fatigue crack growth trajectories and lives. Under equal and proportional loadings on both axes, pure mode I propagation occurs. Mixed mode conditions were simulated using different biaxial load ratios, and mode II propagation can be introduced when different loading phases or mean load values are used. Using an automatic algorithm, different in-phase and out-of-phase loading conditions were simulated in a cruciform specimen. Fatigue life is proportional to initial notch angle β, but inversely proportional to the load phase shift ϕ. The present results increase mixed mode fatigue crack propagation understanding.

Analysis of biaxial proportional low-cycle fatigue crack propagation for hull inclined-crack plate based on accumulative plasticity

Fracture failures of ship plates subjected to in-plane biaxial low-cycle fatigue loading are generally the coupling result of accumulative plasticity and biaxial low-cycle fatigue damage. A biaxial low-cycle fatigue crack growth analysis of hull structure that accounts for the accumulative plasticity effect can be more suitable for the actual evaluation of the overall fracture performance of the hull structure in severe sea conditions. An analytical model of biaxial low-cycle fatigue crack propagation with a control parameter for ∆CTOD is presented for hull inclined-crack plate. A test was conducted for cruciform specimens made of Q235 steel with an inclined crack to validate the presented analysis. The biaxial accumulative plasticity behavior and the effects of biaxiality and stress ratios were investigated. The results of this study reveal a strong dependence of biaxial low-cycle fatigue crack propagation on biaxial accumulated plasticity.

Anti-buckling device for biaxial testing with cruciform specimens

The use of an anti-buckling device is proposed to avoid the appearance of undesired instabilities during biaxial testing with cruciform specimens in which the compressive loads are applied directly on the arms of the sample by means of compression plates. The device consists on a cross-shaped accessory that restricts out-of-plane displacements and a L-shaped support that forces the alignment of the fixture, the specimen and the testing machine. In addition, recommendations about the test methodology and the conditioning of the cruciform sample are given. For this purpose, analytical and numerical studies are developed to design the experiments and to describe both the global buckling of the cruciform specimen and the local instability of the central region subjected to biaxial loading. The risk of instability in the arms of the sample is reduced under tension-compression and compression-compression loading cases whenever the device is used, ensuring that the results are not affected by premature buckling of the specimen and favoring the appearance of appropriate failure modes.

Improving the understanding of how biaxiality ratios correlate on cruciform fatigue test specimens for VHCF ultrasonic fatigue testing

Very High Cycle Fatigue (VHCF) using ultrasonic machines is a subject that is receiving growing attention. Recent developments focus on biaxial stresses which are of interest to industries such as the aeronautical where plane stresses appear in the fuselage and wings. It has been shown before that in-plane cruciform specimens can be changed so that different biaxiality ratios are achieved from equibiaxial to pure shear. This paper analyses how these biaxiality ratios relate to one another between the in-plane orthogonal directions x and y in cruciform specimens. Specimens in this study are composed of Aluminum 6082-T651, a medium strength alloy used in many highly stressed engineering applications, including trusses, cranes, bridges, and transportation. These asymmetric models are purposely designed to develop orthogonal biaxial stresses with non-unitary biaxiality ratios. Comparing the simulation results with the experimental data shows that the strain rates can provide acceptable prediction of biaxiality ratios. Moreover, it was observed that the biaxiality ratios obtained from stress, displacement and strain are not equal and, in fact, can be correlated by an expression that was derived during this research.

Vol4 num4-11 Biaxial testing on CFRP laminates cruciform specimens under compressive loads

A numerical and experimental study is performed on biaxial tests with cruciform specimens in which at least one direction is under compression. Continuous carbon fibre reinforced polymer matrix laminates are studied in angle-ply sequences. The high complexity of the biaxial test is analysed, highlighting the non-linear behavior of the material with pseudo-ductile response. In addition, the presence of compression loads lead to tests in which it is necessary to avoid instabilities in order to obtain adequate results. The numerical simulations based on the Finite Element Method allow to study of the initiation and evolution of the damage in the laminate. The combination of numerical techniques with experimental results, obtained by means of the test instrumentation with strain gauges and Digital Image Correlation, allows to perform a complete characterization of the behaviour of the material in order to achieve less conservative designs of composite structures.

Nonlinear response under several multiaxial loading states in fibre reinforced polymer laminates

The present work includes a summary of the doctoral thesis entitled "Complexity of the structural response of fibre reinforced polymer matrix composites". This PhD thesis focused on analyzing the nonlinear mechanical response of a set of stacking sequences, with main interest in angle-ply laminates, to detail the stress-strain behaviour under a range of loading states: uniaxial tension/compression, loading-unloading-reloading tensile tests, three-point bending and plane stress states. The aim is to delve into the mechanisms of coupling and damage and their influence on the mechanical behaviour, in some cases highly nonlinear, aiming to achieve that the material withstands large strains with the consequent delay of the final failure and the increase in energy absorption capacity. Thanks to the characterization through standard testing, it is possible to calibrate material models based on progressive damage, providing two different numerical approaches which are tested against the different experimentally generated states of plane stress. In addition, it is worth mentioning the biaxial tests on cruciform specimens under different loading ratios, which provide experimental data closer to the actual response of composite structures in service. These tests, due to their greater complexity and lack of standardization, are analyzed in detail by applying numerical simulations and analytical models that ensure the validity of the results, highlighting the possible instabilities generated in the presence of compressive loads.

Characterization of forming limits at fracture from shear to plane strain with a dedicated cruciform specimen

Characterization of forming limits at fracture from shear to plane strain with a dedicated cruciform specimen

Analysis of biaxial proportional low-cycle fatigue and biaxial accumulative plasticity of hull inclined-crack plate

Fracture induced failure of plates in hull structures subjected to in-plane biaxial low-cycle fatigue loading are generally a combination of accumulative plasticity and biaxial low-cycle fatigue damage. A biaxial low-cycle fatigue crack growth analysis of a hull structure that accounts for the accumulative plasticity effect can be suitable for the actual evaluation of the overall fracture induced failure of the hull structure in severe sea conditions. An analytical model of biaxial low-cycle fatigue crack propagation with a control parameter for the J integral was presented for hull inclined-crack plate. The test was conducted for cruciform specimens made of Q235 steel with an inclined crack to validate the presented analysis. The biaxial accumulative plasticity behaviour and the effects of the biaxiality and stress ratios were investigated by numerical analysis. The results of this study reveal a strong dependence of biaxial low-cycle fatigue crack propagation on biaxial accumulated plasticity.

Novel coupled modular steel structure and seismic tests on high-performance interconnection

Modular building registers the advanced stage of construction industrialization and the corner-supported steel modular building is the most widely applied. However, its structure, which is integrated by corner interconnections only, incurs the problems of structural redundancy and interconnection-assembly complexity. To this gap, this paper proposes the novel coupled modular steel structure and suitable interconnection, which significantly affects the overall structural response and assembly efficiency. Pseudo static tests of three full-scale cruciform joint specimens are implemented to study the seismic performance of interconnection. The results show that the currently proposed coupled modular steel structure could replace the incompletely-combined group-columns and laminated beams with single structural components to avoid the structural redundancy and reduce the assembly difficulty of interconnections. The proposed interconnection exhibits excellent seismic performance. Hysteretic loops of coupled beam and module beam are “bow” shape and “shuttle” shape, respectively, indicating their good hysteretic performance. Ultimate storey drift angles of coupled beam and module beam could reach 0.08–0.09 rad and 0.06–0.08 rad, respectively, which satisfy the requirement for SMF in ANSI/AISC 341-16 and indicate their excellent rotation capacity. The ductility coefficients of the specimens are 2.27–3.64 except for MC2, indicating their good ductility capacity. Adopting the flush end plate for coupled beam and high strength bolts for vertical splice is recommended for the interconnections to obtain better hysteretic performance and bearing capacity. This research provides brand new design for modular construction and references for future research on global response of coupled modular steel structure.

A PD-FEM coupling approach for modeling thermal fractures in brittle solids

A novel approach coupling peridynamic (PD) and finite element method (FEM) is initiated to investigate the onset and development of thermal fractures in brittle solids. In this technique, the analysis domain is divided into two separate layers, of which the thermal diffusion equation is solved in the FEM layer, while the solid deformation, even fracturing, is represented by the peridynamics layer. The temperature related quantities are applied locally within the FEM layer, and the resulting thermal strain is then used in the PD layer. The noteworthy features of the proposed PD-FEM coupling approach include: (1) it is a straightforward application of classical thermal diffusion equation using the FEM, and thus it is free of any calibration procedure to determine the PD micro-conductivity coefficients, and (2) it is computationally flexible in the sense that the discretization of each layer is not necessarily identical. The coupled model is solved by a staggered solution scheme. By comparing with available closed-form solutions and reference solutions by the pure FEM model, the accuracy of the coupling approach is evaluated firstly. Then the coupled model is used for modeling a notched cruciform specimen under mechanical-thermal loading and ceramics under thermal shock to demonstrate its ability to reproduce the complex crack patterns involving heat transfer.

Development of a biaxial tensile device in the plane for monotonic mechanical tests and cruciform specimens / Desenvolvimento de um dispositivo de tração biaxial no plano para ensaios mecânicos monotônicos e de corpos de prova cruciformes

This work deals with the development of a coupling device for performing biaxial tensile tests with cruciform specimens. For the project, a methodology consisting of six phases was used, that is, informational design, conceptual design, preliminary design, detailed design, manufacturing and testing. Thus, the design and sizing of two coupling devices was carried out, and the model chosen for manufacturing was based on that proposed by Rohr, Harwick, and Nahme. In addition, the design, sizing and fabrication of cruciform specimens in MDF and PS, with geometry similar to that of ISO 16842:2014, was also carried out for the device validation tests. The tests were divided into 1) device stiffness test and 2) specimen deformation test for equibiaxial testing. The proposed test setup was designed to test cruciform specimens with dimensions up to 350 x 350 x 4 mm and support a maximum vertical load of up to 30 kN.